Most Dutch people who use a bike as part of their transit routine leave it at a station. It's common to have one bike at home and another bike at a station near your work.
You ride your first bike to the station, get on the public transit, then ride your second bike to work. Then there's no need to take your bike on public transit.
You ride your first bike to the station, get on the public transit, then ride your second bike to work. Then there's no need to take your bike on public transit.